A Monte Carlo comparison of the Type I and Type II error rates of tests of multivariate normality

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On tests for multivariate normality and associated simulation studies (2007, methodology): “In addition to their extensive simulation study involving a power comparison of 13 different approaches for a wide variety of alternative distributions, they [5] also cite refs.”
A Generalization of Shapiro–Wilk's Test for Multivariate Normality (2009, background): “Mecklin and Mundfrom (2005) and Farrell et al. (2007) recommended Henze and Zirkler’s (1990) test as a formal goodness of fit test.”
Robust factor analysis in the presence of normality violations, missing data, and outliers: Empirical questions and possible solutions (2014, methodology): “Mecklin and Mundfrom (2005) categorised MVN tests into four groups: Graphical and correlational approaches (e.g. chi-squared plot), Skewness and kurtosis approaches (e.g. Mardia's tests of skewness and kurtosis), Goodness of fit approaches (e.g. omnibus tests), and Consistent approaches (e.g.…”